# Questions tagged [bivariate-distributions]

For questions on bivariate distributions, the combined probability distribution of two randomly different variables.

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### showing that a r.v. is a bivariate normal distribution…

A bullet is fired at a target. (X,Y) is a bivariate normal random variable that represent the horizontal and vertical distance from the center of the target where the bullet strikes the target when ...
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### Joint distribution of sum of random variables in bivariate distribution

We have the following bivariate distribution: $$f(x,y) = e^{-(\theta x + y/\theta)}$$ for x,y >0. We would like to find the distribution of $$\left(\sum_{i=1}^n X_i, \sum_{i=1}^n Y_i\right)$$ I'm not ...
### Finding $P(X+Y \geq 0.5)$ given $f(x,y) = x - y + 1$ for $0 \leq x, y \leq 1$
For the bivariate density function (not necessarily independent) $$f(x,y) = x - y + 1$$ for $$0 \leq x, y \leq 1$$ I am trying to find $\Pr(X+Y \geq 0.5)$. I integrated $y$ across $0.5-x$ to $1$ ...